The Ascending Double-Cone: A Closer Look at a Familiar Demonstration

The double-cone ascending an inclined V-rail is a common exhibit used for demonstrating concepts related to center-of-mass in introductory physics courses. While the conceptual explanation is well-known--the widening of the ramp allows the center of mass of the cone to drop, overbalancing the increase in altitude due to the inclination of the ramp--there remains rich physical content waiting to be extracted through deeper exploration. Such an investigations seems to be absent from the literature. This article seeks to remedy the omission.Comment: LaTeX, 16 pages, 18 eps figure

Inversion of Gamow\u27s formula and inverse scattering

Gamow\u27s tunneling formula is inverted and the issue of the uniqueness of the solution is compared with the solution obtained by the method of Gel\u27fand and Levitan. Some insight is gained into the key differences between classical and quantum inverse scattering, which account for the fact that a potential can be uniquely determined in the latter but only to within a symmetry family in the former. (C) 2006 American Association of Physics Teachers

Inversion of Gamow's Formula and Inverse Scattering

We present a pedagogical description of the inversion of Gamow's tunnelling formula and we compare it with the corresponding classical problem. We also discuss the issue of uniqueness in the solution and the result is compared with that obtained by the method of Gel'fand and Levitan. We hope that the article will be a valuable source to students who have studied classical mechanics and have some familiarity with quantum mechanics.Comment: LaTeX, 6 figurs in eps format. New abstract; notation in last equation has been correcte